This invention relates to identifying most likely errors in a communication signal and, more particularly, to identifying potential error locations, patterns, and likelihood metrics in connection with trellis-based detection and/or decoding. This invention also relates to computing soft reliability information for each detected/decoded bit or codeword syndrome value.
Consider a system that can be represented by a finite state machine. For example, a finite state machine can be used to model an inter-symbol-interference (ISI) channel or a convolutional code encoder. A trellis diagram can be used to represent the sequence of all possible paths (i.e., sequences of states) that the system can visit over time. If the system can transition from state A at time t to state B at time t+1, then these states are connected by a branch. Each branch may be labeled by X/Y pair, where X denotes the input that causes the system to transition from state A to B and Y represents an output corresponding to this transition. For example, an ISI channel with a two-bit channel response can be represented by a four-state trellis diagram. The states of this trellis can be labeled as 00, 01, 10, 11 and may be associated with the latest two bits transmitted through the ISI channel. For example, if the system is at state 01 at time t, and 0 is transmitted, then the next state at time t+1 would be 10. Similarly, the system would transition to state 11 if 1 were transmitted. Channel output Y that results from these transitions is a real number m, that may be different for each branch.
In the convolutional encoding situation, an encoder receives input bits and generates output bits that are weighted sums of the input bits.
In the case of an ISI channel, the number of output signals will be usually the same as the number of input signals. In contrast, a convolutional encoder generally does introduce additional output bits, such that there may be two bits at the output of a convolutional encoder for each input bit, for example.
In the ISI channel situation, the signals at the output of the ISI channel are detected by a trellis-based detector, such as a Viterbi (maximum-likelihood) detector. In the convolutional encoder situation, the bits at the output of the encoder (also called “parity bits”) are communicated to a receiver and are decoded using a Viterbi decoder. In either situation, the detector/decoder is based on the trellis representing the ISI channel or the convolutional encoder. However, a Viterbi detector/decoder does not know the particular path that occurred in the trellis of the ISI channel/convolutional encoder. Rather, the Viterbi detector/decoder must use the signals/bits it receives and find the trellis path that most-likely occurred based on the received signals/bits. This detection/decoding is often complicated by the presence of noise or errors in the received signals/bits. In some situations, the trellis path that most-likely occurred based on the received signals/bits may not be the same as the trellis path that actually occurred in the ISI channel/convolutional encoder. In such situations, another layer of error-correction may be applied before the ISI channel/convolutional encoding, so that any errors that may remain after Viterbi detection/decoding can be addressed. In this case, it may be helpful to determine the potential location and nature of these errors and to provide this information to the additional layer of error-correction for its consideration.